Results 1  10
of
23
A coinductive calculus of streams
, 2005
"... We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analo ..."
Abstract

Cited by 27 (9 self)
 Add to MetaCart
We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analogy to classical analysis, the latter are presented as behavioural differential equations. A number of applications of the calculus are presented, including difference equations, analytical differential equations, continued fractions, and some problems from discrete mathematics and combinatorics.
Properties of phylogenetic trees generated by Yuletype speciation models
 Math. Biosci
, 2001
"... We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Firstly, for a rooted tree generated by the Yule model we describe the probability distribution on the depth �number of edges from the root) of the most recent common ancestor of a random subset of k species. Next we show that, for trees generated under the Yule model, the approximate position of the root can be estimated from the associated unrooted tree, even for trees with a large number of leaves. Finally, we analyse a biologically motivated extension of the Yule model and describe its distribution on tree shapes when speciation occurs
Exact Potts model partition functions for strips of the triangular lattice
 J. Stat. Phys
"... We present exact calculations of the partition function of the qstate Potts model on (i) open, (ii) cyclic, and (iii) Möbius strips of the honeycomb (brick) lattice of width Ly = 2 and arbitrarily great length. In the infinitelength limit the thermodynamic properties are discussed. The continuous ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
We present exact calculations of the partition function of the qstate Potts model on (i) open, (ii) cyclic, and (iii) Möbius strips of the honeycomb (brick) lattice of width Ly = 2 and arbitrarily great length. In the infinitelength limit the thermodynamic properties are discussed. The continuous locus of singularities of the free energy is determined in the q plane for fixed temperature and in the complex temperature plane for fixed q values. We also give exact calculations of the zerotemperature partition function (chromatic polynomial) and W(q), the exponent of the groundstate entropy, for the Potts antiferromagnet for honeycomb strips
Integrals over Grassmannians and Random permutations
, 2001
"... In testing the independence of two Gaussian populations, one computes the distribution of the sample canonical correlation coefficients, given that the actual correlation is zero. The “Laplace transform” of this distribution is not only an integral over the Grassmannian of pdimensional planes in co ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
In testing the independence of two Gaussian populations, one computes the distribution of the sample canonical correlation coefficients, given that the actual correlation is zero. The “Laplace transform” of this distribution is not only an integral over the Grassmannian of pdimensional planes in complex nspace, but is also related to a generalized hypergeometric function. Such integrals are solutions of Painlevélike equations. They also have expansions, related to random words of length ℓ formed with an alphabet of p letters. Given that each letter appears in the word, the maximal length of the disjoint union of p increasing subsequences of the word clearly equals ℓ. But the maximal length of the disjoint union of p − 1 increasing subsequences leads to a nontrivial distribution. It is precisely this
A solution of the isomorphism problem for circulant graphs
 Proc. London Math. Soc
, 2004
"... All graphs considered in the paper are directed. Let be a graph on n vertices which we identify with the elements of the additive cyclic group Z n f0; 1;...;n 1g. The graph is called circulant if it has a cyclic symmetry, that is, if the permutation ð0; 1; 2;...;n 1Þ is anautomorphism of the graph. ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
All graphs considered in the paper are directed. Let be a graph on n vertices which we identify with the elements of the additive cyclic group Z n f0; 1;...;n 1g. The graph is called circulant if it has a cyclic symmetry, that is, if the permutation ð0; 1; 2;...;n 1Þ is anautomorphism of the graph.
Coxeter groups and hyperbolic manifolds
 Math. Ann
"... The date of receipt and acceptance will be inserted by the editor 1 ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
The date of receipt and acceptance will be inserted by the editor 1
Counting Lattice Triangulations
 Surveys in Combinatorics 2003, number 307 in Lond. Math. Soc. Lect. Note Ser
, 2003
"... We discuss the problem to count, or, more modestly, to estimate the number f(m, n) of unimodular triangulations of the planar grid of size m n. ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We discuss the problem to count, or, more modestly, to estimate the number f(m, n) of unimodular triangulations of the planar grid of size m n.
Deformation of Weyl Modules and Generalized Parking Functions
 IMRN 2004
"... Abstract. Local Weyl modules over twodimensional currents with values in glr are deformed into spaces with bases related to parking functions. Using this construction we 1) reproof that dimension of the space of diagonal coinvariants is not less than the number of parking functions; 2) describe the ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. Local Weyl modules over twodimensional currents with values in glr are deformed into spaces with bases related to parking functions. Using this construction we 1) reproof that dimension of the space of diagonal coinvariants is not less than the number of parking functions; 2) describe the limit of Weyl modules in terms of semiinfinite forms and find the limit of characters; 3) propose a lower bound and state a conjecture for dimensions of Weyl modules with arbitrary highest weights. Also we express characters of deformed Weyl modules in terms of ρparking functions and the Frobenius characteristic map.
WEIGHT MULTIPLICITY POLYNOMIALS OF MULTIVARIABLE WEYL MODULES
, 2009
"... This paper is based on the observation that dimension of weight spaces of multivariable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable cases and discuss the underlying combinatorics. ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
This paper is based on the observation that dimension of weight spaces of multivariable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable cases and discuss the underlying combinatorics.
Notes on HilbertKunz multiplicity of Rees algebras
"... Abstract. In this paper, we estimate the HilbertKunz multiplicity of the (extended) Rees algebras in terms of some invariants of the base ring. Also, we give an explicit formula for the HilbertKunz multiplicities of Rees algebras over Veronese subrings. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. In this paper, we estimate the HilbertKunz multiplicity of the (extended) Rees algebras in terms of some invariants of the base ring. Also, we give an explicit formula for the HilbertKunz multiplicities of Rees algebras over Veronese subrings.